This invention relates to an optical imaging system used in an image transmission portion of, for example, a facsimile device or a copier.
Optical imaging systems which include a plurality of rod lenses with a refractive index distribution in a radial direction and are arranged in an array, and those that contain a homogeneous lens array of convex microlenses that are arranged regularly and have a predetermined curvature on their front and back sides are widely used in the image transmission portion of, for example, facsimile devices or copiers.
Lenses used for rod lens arrays often have diameters of 0.6 to 1.1 mm, and a resolving power demanded from such a rod lens array called for an MTF (modulation transfer function) of at least 60% when a pattern of spatial frequency of 4-6 line-pairs / mm(ca. 200 dpi-300 dpi) is imaged.
The refractive index distribution of such rod lenses can be expressed as:
n(r)2=n02xc2x7{1xe2x88x92(gxc2x7r)2+h4xc2x7(gxc2x7r)4+h6xc2x7(gxc2x7r)6}xe2x80x83xe2x80x83Eq. 1
wherein r is the radial distance from the optical axis of the rod lens, n(r) is the refractive index at the radial distance r from the optical axis of the rod lenses, n0 is the refractive index at the optical axis of the rod lens (center refractive index), and g, h4 and h6 are coefficients for the refractive index distribution.
The brightness of the rod lenses depends mainly on the aperture angle xcex8 (xc2x0), which can be expressed by
xcex8=(n0xc2x7gxc2x7r0)/(xcfx80/180).xe2x80x83xe2x80x83Eq. 2
wherein r0 is the radius of the portion of the rod lenses functioning as a lens.
The larger the aperture angle xcex8 is, the brighter the achieved image and the shorter the time required for scanning. The largest aperture angle xcex8 found in available rod lenses is 23xc2x0.
In the case of rod lenses used for one-to-one imaging, spherical aberration and image surface curvature are the main cause of deterioration of the resolving power. Spherical aberration on the optical axis can be corrected by optimizing the refractive index distribution. However, since rod lenses consist basically only of convex lenses, the Petzval sum becomes large, and thus the image surface curvature cannot be corrected. In addition, because a plurality of lens images are superimposed in a rod lens array, blurred images are superimposed on each other when there is image surface curvature, which leads to a considerable deterioration of the resolving power. Because the image surface curvature is proportional to the square of the aperture angle xcex8, as the aperture angle increases (that is, the brighter the lens is), the influence of image surface curvature increases.
Recently, because of the improved image quality of printers and scanner, a resolving power of at least 12 line-pair/mm (ca. 600 dpi) is demanded of such rod lens arrays. Therefore, it is necessary to suppress the image surface curvature to a minimum in order to improve the resolving power.
There are two methods for reducing the image surface curvature to improve the resolving power. A first method is to use rod lenses with a small aperture angle xcex8. For example, if the diameter of the rod lenses is 0.6 mm, and the aperture angle is 10xc2x0 or less, the influence of the image surface curvature is so small that it can be ignored. However, reducing the aperture angle xcex8 makes the image darker, which causes the problem of longer scanning times.
A second method for reducing the image surface curvature to improve the resolving power is to reduce the diameter of the rod lenses. The variation of the focal point due to image surface curvature becomes smaller in proportion with the diameter of the rod lenses, so that the resolving power can be improved even when bright rod lenses with a large aperture angle xcex8 are used. However, when the diameter of the rod lenses is reduced, the distance WD between the rod lenses and the image plane becomes small, so that there is the problem that there is too little space to arrange for an illumination system or a sensor device. Moreover, the precision required for assembling the rod lens array becomes extreme, which becomes a factor for rising costs.
Besides rod lens arrays, homogenous lens arrays, in which roof lens arrays of convex lenses aligned with a reflector or two lens array plates in which convex microlenses are arranged regularly in the front side and back side of a transparent plate with a uniform refractive index are aligned, are also known as optical elements for one-to-one imaging. However, since these optical elements as well consist basically only of convex lenses, the Petzval sum becomes large, as pointed out above, and there is the same problem of lower resolving power due to image surface curvature as in rod lens arrays with refractive index distribution.
Moreover, if an erect one-to-one image is to be attained by using a homogenous lens array, adjacent lenses have to be separated, so as to prevent the adverse effect of transfer images due to stray light from adjacent lenses entering the lens faces arranged on one optical axis. For this case, Publication of Unexamined Japanese Patent Application No. Sho 55-90908 discloses a method, in which the lenses arranged on the optical axis are rod-shaped, and separated by a different material disposed between the rod lenses.
However, homogenous erect one-to-one lens arrays using rod lenses have a complex configuration, and rising costs due to complex steps and performance variations caused by their assembly cannot be avoided.
The present invention has been achieved in order to solve the above-mentioned problems of the prior art, and its object is to provide an optical imaging system whose resolving power can be improved by eliminating image portions with large image surface curvature. It is a further object of the present invention to provide an optical imaging system for erect one-to-one imaging using a homogenous material that can be easily molded into a lens array, and in which stray light does not enter adjacent lenses.
In order to attain these objects, an optical imaging system for focusing light from an object plane onto an image plane in accordance with the present invention includes a lens array having a plurality of optical lens systems that are arranged in at least one row with optical axes of the lens systems in parallel; and further includes, at least in a longitudinal direction of the lens array, means for blocking light rays that pass through the lens faces of the optical lens systems at an angle larger than a predetermined angle with respect to the optical axes of the optical lens systems. With this configuration, light rays that pass through the lens faces of the optical lens systems at an angle larger than a predetermined angle with respect to the optical axes of the optical lens systems are blocked in a longitudinal direction of the lens array, so that the aperture angle becomes smaller. Thus, a portion of the image with large image surface curvature is eliminated, and the resolving power of the lens array is improved.
In this configuration of an optical imaging system, it is preferable that light rays that pass through the lens faces of the optical lens systems are not blocked in a direction that is perpendicular to the longitudinal direction of the lens array.
In this configuration of an optical imaging system, it is also preferable that the optical lens systems include rod lenses having a refractive index distribution in a radial direction. It is also preferable that both edge portions of the rod lenses in the longitudinal direction of the lens array are shaved off along the optical axis of the rod lenses. In this configuration, light rays that pass through the lens faces of the optical lens systems at an angle larger than a predetermined angle with respect to the optical axes of the optical lens systems are blocked in a longitudinal direction of the lens array, so that the aperture angle becomes smaller. Thus, a portion of the image with large image surface curvature is eliminated, and the resolving power of the lens array is improved. In this case, it is even more preferable that ry/r0 is in the range given by
0.1xe2x89xa6ry/r0xe2x89xa60.8
wherein r0 is the radius of the portion of the rod lenses functioning as a lens, and 2ry is the length in the longitudinal direction of the lens array of the rod lenses after both edge portions of the rod lenses in the longitudinal direction of the lens array have been shaved off along the optical axis of the rod lenses. If ry/r0 is less than 0.1, the rod lenses become too narrow and the number of rod lenses that are necessary for the rod lens array becomes too large. If r0/ry exceeds 0.8, the remaining image surface curvature becomes large, so that the resolving power deteriorates. Preferably, when rod lenses are used, pairs of cut-outs are provided that oppose each other in a substantially central portion in the direction of the optical axes of the rod lenses, and the normals of the faces of the cut-outs that oppose each other point into the longitudinal direction of the lens array. With this configuration, a resin or the like can be filled into the cut-outs of the rod lenses when assembling the lens array, so that light rays are blocked in the longitudinal direction of the lens array that are affiliated with the image portions with a large image curvature, and the aperture angle is reduced. As a result, the image portion with a large image surface curvature is eliminated, which improves the resolving power when using the rod lens array. In this case, it is even more preferable that ry/r0 is in the range given by
0.1xe2x89xa6ry/r0xe2x89xa60.8
wherein r0 is the radius of the portion of the rod lenses functioning as a lens, and 2ry is the distance between the opposing faces of the pairs of cut-outs.
If rod lenses with a refractive index distribution are used for the one-to-one optical imaging systems, it is preferable that the refractive index distribution of the rod lenses is
n(r)2=n02xc2x7{1xe2x88x92(gxc2x7r)2+h4xc2x7(gxc2x7r)4+h6xc2x7(gxc2x7r)6}
wherein r is the radial distance from the optical axis of the rod lenses, n0 is the refractive index at the optical axis of the rod lenses, and g, h4 and h6 are coefficients for a refractive index distribution. In this case, it is also preferable that the aperture angle xcex8 of the rod lenses, which is defined as xcex8=(n0xc2x7gxc2x7r0)/(xcfx80/180), is in the range given by 4xc2x0xe2x89xa6xcex8xe2x89xa640xc2x0. In this case, it is furthermore preferable that the refractive index n0 at the optical axis of the rod lenses is in the range given by 1.4xe2x89xa6n0xe2x89xa61.9. In this case, it is also preferable that Z0/P is in the range given by 0.5xe2x89xa6Z0/P xe2x89xa61.0, wherein Z0 is the length of the rod lenses and P=2xcfx80/g is a one-pitch length of the rod lenses.
With these preferable configurations, erect imaging is possible. Moreover, except for the case that both edge portions of the rod lenses in the longitudinal direction of the lens array are shaved off along the optical axes of the rod lenses, it is also preferable that r0/R is in the range given by 0.5xe2x89xa6r0Rxe2x89xa6=1.0, wherein r0 is the radius of the portion of the rod lens functioning as a lens, and 2R is the distance 2R between the optical axes of two adjacent rod lenses.
In the above-mentioned configuration of an optical imaging system in accordance with the present invention, it is preferable that the means for blocking light rays include aperture stops provided in at least one space selected from a space between the lens array and the object plane and a space between the lens array and the image plane. With this configuration, light rays that pass through the lens faces of the optical lens systems at an angle that is larger than a predetermined angle with respect to the optical axes of the optical lens systems are blocked in a longitudinal direction of the lens array, so that the aperture angle becomes smaller. Thus, a portion of the image with large image surface curvature is eliminated, and the resolving power of the lens array is improved. In this case, in accordance with one or more embodiments, it is preferable that the aperture stops are substantially rectangular. Also, in this case, in accordance with one or more embodiments, it is preferable that the aperture stops are substantially elliptical. Further, in accordance with one or more embodiments, it is preferable that the aperture stops are provided at a distance from and end face of the optical lens systems. With this configuration, light rays associated with large image surface curvature can be blocked, while occupying a large effective surface area of the lens. In this case, it is also preferable that the thickness of the aperture stops in the direction of the optical axes of the lenses is in the range of r0 to 5r0, where r0 is the radius of the portion of the rod lenses functioning as a lens. In this case, it is also preferable that the aperture stops are provided in multiple stages. With this configuration, the same effect as with thick aperture stops can be attained, while using thin aperture stops for each stage, so that more precise perforations are possible. In this case, it is also preferable that the aperture stops are formed by blackening a surface of a transparent plate with a printed pattern. With this configuration, a pattern with more precise dimensions can be manufactured at lower costs than when thin plates with perforations are used. In this case, it is preferable that the optical lens systems are rod lenses with a refractive index distribution in the radial direction, and ry/r0 is in the range given by
0.1xe2x89xa6ry/r0xe2x89xa60.9
wherein r0 is the radius of the portion of the rod lenses functioning as a lens, and ry is the effective radius of the rod lenses, which are restricted by the aperture stops, in the longitudinal direction of the lens array. In this case, it is preferable that the refractive index distribution of the rod lenses is
n(r)2=n02xc2x7{1xe2x88x92(gxc2x7r)2+h4xc2x7(gxc2x7r)4+h6xc2x7(gxc2x7r)6}
wherein r is the radial distance from the optical axis of the rod lenses, n0 is the refractive index at the optical axis of the rod lenses, and g, h4 and h6 are coefficients for a refractive index distribution. In this case, it is also preferable that the aperture angle xcex8 of the rod lenses, which is defined as xcex8=(n0xc2x7gxc2x7r0)/(xcfx80/180), is in the range given by 4xc2x0xe2x89xa6xcex8xe2x89xa640xc2x0. In this case, it is furthermore preferable that the refractive index n0 at the optical axis of the rod lenses is in the range given by 1.4xe2x89xa6n0xe2x89xa61.9. In this case, it is also preferable that Z0/P is in the range given by 0.5xe2x89xa6Z0/P xe2x89xa61.0, wherein Z0 is the length of the rod lenses and P=2xcfx80/g is a one-pitch length of the rod lenses. Moreover, except for the case that both edge portions of the rod lenses in the longitudinal direction of the lens array are shaved off along the optical axes of the rod lenses, it is also preferable that r0/R is in the range given by 0.5xe2x89xa6r0/Rxe2x89xa61.0, wherein r0 is the radius of the portion of the rod lens functioning as a lens, and 2R is the distance 2R between the optical axes of two adjacent rod lenses.
In the above-mentioned configuration of an optical imaging system in accordance with one or more embodiments of the present invention, it is preferable that the lens array includes an erect one-to-one lens array, in which two homogenous lens array plates are stacked on top of each other, with microlenses, whose front and back surface have a certain curvature and which function as convex lenses, being arranged regularly in the two homogenous lens array plates.
In the above-mentioned configuration of an optical imaging system in accordance with the present invention, it is preferable that the means for blocking light rays include light-blocking plates disposed in at least one space selected from the group consisting of the space between the lens array and the object plane and the space between the lens array and the image plane. With this configuration, light rays that pass through the lens faces of the optical lens systems at an angle that is larger than a predetermined angle with respect to the optical axes of the optical lens systems are blocked in a longitudinal direction of the lens array, so that the aperture angle becomes smaller. Thus, a portion of the image with large image surface curvature is eliminated, and the resolving power of the lens array is improved. In this case, it is preferable that the light-blocking plates are arranged periodically in a longitudinal direction of the lens array. When the light-blocking plates are arranged in an irregular fashion, irregularities in the light amount may result. In this case, it is preferable that the light-blocking plates are flat and the light-blocking plates are arranged at constant intervals in the longitudinal direction of the lens array. Furthermore, it is preferable that a space between adjacent light-blocking plates is filled with a transparent medium. With this configuration, not only can the light-blocking plates be made extremely thin, but it is also possible to prevent bending of the light-blocking plates and irregularities in the spacing. Furthermore, it is preferable that the light-blocking plates are provided at a distance from an end face of the optical lens systems. With this configuration, irregularities in the light amount caused by the pitch between the light-blocking plates can be lessened. Furthermore, it is preferable that the thickness of the light-blocking plates in the longitudinal direction of the lens array is not more than ⅕ of the pitch length of the intervals of the light-blocking plates. Furthermore, it is preferable that the interval pitch of the light-blocking plates is smaller than the pitch of the optical lens systems. With this configuration, periodic irregularities in the image brightness can be prevented. In this case it is even more preferable that the lens array is a homogenous erect one-to-one lens array, in which two homogenous lens array plates are stacked on top of each other, with microlenses, whose front and back surface have a certain curvature and which function as convex lenses, being arranged regularly in the two homogenous lens array plates, and the lens array is made by injection molding. With this configuration, stray light can be prevented by eliminating light rays with an angle that is larger than the aperture angle that enter the homogenous erect one-to-one lens array or leave the homogenous erect one-to-one lens array. As a result, the contrast of the image is improved, so that the transmission of a high quality image becomes possible. Moreover, setting light-blocking plates in front of a homogenous erect one-to-one lens array made by molding lenses in one piece allows a considerable reduction in production costs, because this achieves similar or better properties as with a lens array for homogenous erect one-to-one imaging in which a plurality of columnar rod lenses is arranged in a row with their optical axes in parallel.
In the above-mentioned configuration, it is preferable that the optical imaging system is provided with means for blocking, in the longitudinal direction of the lens array and in a direction that is perpendicular to the longitudinal direction of the lens array, light rays that pass through the lens faces of the optical lens systems at an angle that is larger than a predetermined angle with respect to the optical axes of the optical lens systems. In this case, it is preferable that the means for blocking light rays include light-blocking plates provided in at least one space selected from the group consisting of the space between the lens array and the object plane and the space between the lens array and the image plane, and the light-blocking plates are arranged periodically in two dimensions in a direction parallel to the object plane and the image plane. It is preferable that a space between adjacent light-blocking plates is filled with a transparent medium. It is also preferable that the light-blocking plates are disposed at a distance from an end face of the optical lens systems. Also, it is preferable that the light-blocking plates are honeycomb shaped. The reason for this is that with a honeycomb-shape, the difference in the restriction angles depends only little on the orientation, the plates can be made thin, and such a shape is easy to manufacture.